Enhanced power method on an electronic device

ABSTRACT

A power method can be enhanced. For example, an electronic communication indicating a job to be performed can be received. A best rank-1 approximation of a matrix associated with the job can be determined using the power method. Each iteration of the power method can include determining a point that lies on a line passing through (i) a first value for a first singular vector from an immediately prior iteration of the power method; and (ii) a second value for the first singular vector from another prior iteration of the power method. Each iteration of the power method can also include determining, by performing the power method using the point, a current value for the first singular vector and a current value for a second singular vector for a current iteration of the power method. The job can then be performed using the best rank-1 approximation of the matrix.

REFERENCE TO RELATED APPLICATION

This claims the benefit of priority under 35 U.S.C. §119(e) to U.S.Provisional Patent Application No. 62/344,717 filed Jun. 2, 2016, theentirety of which is hereby incorporated by reference herein.

TECHNICAL FIELD

The present disclosure relates generally to electrical computers anddigital data processing systems. More specifically, but not by way oflimitation, this disclosure relates to an enhanced power method on anelectronic device.

BACKGROUND

Machine-learning classifiers (e.g., neural networks), predictive models,and statistical models can apply hundreds of thousands of operations todata sets to determine information about the data sets. It can take asignificant amount of time, memory, processing power, and electricalpower to perform these operations. For example, a computing device mayperform thousands of matrix operations over hundreds of iterations ofsteps to analyze a data set, during which time the computing device mayrepeatedly access and store information in thousands of memorylocations. This level of processing can take hours, or days, to perform;can require a significant amount of electrical power; can reduce theavailable resources (e.g., processing power and memory) on the computingdevice for performing other tasks; can slow down other processesexecuting on the computing device; and can require complicated andexpensive hardware.

SUMMARY

In one example, a non-transitory computer readable medium comprisingprogram code that is executable by a processor is provided. The programcode can cause the processor to receive an electronic communicationindicating a job to be performed. The program code can cause theprocessor to determine a best rank-1 approximation of a matrixassociated with the job using a power method. Each iteration of thepower method can include determining a point that lies on a line passingthrough (i) a first value for a first singular vector from animmediately prior iteration of the power method; and (ii) a second valuefor the first singular vector from another prior iteration of the powermethod. Each iteration of the power method can also include determining,by performing the power method using the point, a current value for thefirst singular vector and a current value for a second singular vectorfor a current iteration of the power method. The program code can causethe processor to perform the job at least in part using the best rank-1approximation of the matrix. The program code can cause the processor totransmit another electronic communication associated with a result ofthe job.

In another example, a method is provided that can include receiving anelectronic communication indicating a job to be performed. The methodcan including determining a best rank-1 approximation of a matrixassociated with the job using a power method. Each iteration of thepower method can include determining a point that lies on a line passingthrough (i) a first value for a first singular vector from animmediately prior iteration of the power method; and (ii) a second valuefor the first singular vector from another prior iteration of the powermethod. Each iteration of the power method can also include determining,by performing the power method using the point, a current value for thefirst singular vector and a current value for a second singular vectorfor a current iteration of the power method. The method can includeperforming the job at least in part using the best rank-1 approximationof the matrix. The method can include transmitting another electroniccommunication associated with a result of the job.

In another example, a system is provided that can include a processingdevice and a memory device. The memory device can include instructionsexecutable by the processing device for causing the processing device toreceive an electronic communication indicating a job to be performed.The instructions can cause the processing device to determine a bestrank-1 approximation of a matrix associated with the job using a powermethod. Each iteration of the power method can include determining apoint that lies on a line passing through (i) a first value for a firstsingular vector from an immediately prior iteration of the power method;and (ii) a second value for the first singular vector from another prioriteration of the power method. Each iteration of the power method canalso include determining, by performing the power method using thepoint, a current value for the first singular vector and a current valuefor a second singular vector for a current iteration of the powermethod. The instructions can cause the processing device to perform thejob at least in part using the best rank-1 approximation of the matrix.The instructions can cause the processing device to transmit anotherelectronic communication associated with a result of the job.

This summary is not intended to identify key or essential features ofthe claimed subject matter, nor is it intended to be used in isolationto determine the scope of the claimed subject matter. The subject mattershould be understood by reference to appropriate portions of the entirespecification, any or all drawings, and each claim.

The foregoing, together with other features and examples, will becomemore apparent upon referring to the following specification, claims, andaccompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure is described in conjunction with the appendedfigures:

FIG. 1 is a block diagram of an example of the hardware components of acomputing system according to some aspects.

FIG. 2 is an example of devices that can communicate with each otherover an exchange system and via a network according to some aspects.

FIG. 3 is a block diagram of a model of an example of a communicationsprotocol system according to some aspects.

FIG. 4 is a hierarchical diagram of an example of a communications gridcomputing system including a variety of control and worker nodesaccording to some aspects.

FIG. 5 is a flow chart of an example of a process for adjusting acommunications grid or a work project in a communications grid after afailure of a node according to some aspects.

FIG. 6 is a block diagram of a portion of a communications gridcomputing system including a control node and a worker node according tosome aspects.

FIG. 7 is a flow chart of an example of a process for executing a dataanalysis or processing project according to some aspects.

FIG. 8 is a block diagram including components of an Event StreamProcessing Engine (ESPE) according to some aspects.

FIG. 9 is a flow chart of an example of a process including operationsperformed by an event stream processing engine according to someaspects.

FIG. 10 is a block diagram of an ESP system interfacing between apublishing device and multiple event subscribing devices according tosome aspects.

FIG. 11 is a flow chart of an example of a process for enhancing a powermethod on an electronic device according to some aspects.

FIG. 12 is a flow chart of an example of a process for determining abest rank-1 approximation of a matrix associated with a job according tosome aspects.

FIG. 13 is a table of an example of results using a traditional powermethod according to some aspects.

FIG. 14 is a table of an example of results using an enhanced powermethod according to some aspects.

FIG. 15 is a table of an example of computational costs for performing atraditional power method and for performing an enhanced power methodaccording to some aspects.

FIG. 16 is a table of an example of data sets for comparing atraditional power method to an enhanced power method according to someaspects.

FIG. 17 is a table of an example of results from analyzing the data setsin FIG. 16 using the traditional power method and the enhanced powermethod according to some aspects.

In the appended figures, similar components or features can have thesame reference label. Further, various components of the same type canbe distinguished by following the reference label by a dash and a secondlabel that distinguishes among the similar components. If only the firstreference label is used in the specification, the description isapplicable to any one of the similar components having the same firstreference label irrespective of the second reference label.

DETAILED DESCRIPTION

In the following description, for the purposes of explanation, specificdetails are set forth in order to provide a thorough understanding ofexamples of the technology. But various examples can be practicedwithout these specific details. The figures and description are notintended to be restrictive.

The ensuing description provides examples only, and is not intended tolimit the scope, applicability, or configuration of the disclosure.Rather, the ensuing description of the examples provides those skilledin the art with an enabling description for implementing an example.Various changes may be made in the function and arrangement of elementswithout departing from the spirit and scope of the technology as setforth in the appended claims.

Specific details are given in the following description to provide athorough understanding of the examples. But the examples may bepracticed without these specific details. For example, circuits,systems, networks, processes, and other components can be shown ascomponents in block diagram form to prevent obscuring the examples inunnecessary detail. In other examples, well-known circuits, processes,algorithms, structures, and techniques may be shown without unnecessarydetail in order to avoid obscuring the examples.

Also, individual examples can be described as a process that is depictedas a flowchart, a flow diagram, a data flow diagram, a structurediagram, or a block diagram. Although a flowchart can describe theoperations as a sequential process, many of the operations can beperformed in parallel or concurrently. In addition, the order of theoperations can be re-arranged. A process is terminated when itsoperations are completed, but can have additional operations notincluded in a figure. A process can correspond to a method, a function,a procedure, a subroutine, a subprogram, etc. When a process correspondsto a function, its termination can correspond to a return of thefunction to the calling function or the main function.

Systems depicted in some of the figures can be provided in variousconfigurations. In some examples, the systems can be configured as adistributed system where one or more components of the system aredistributed across one or more networks in a cloud computing system.

Certain aspects and features of the present disclosure relate toimproving processing speeds and reducing an amount of memory used by anelectronic device to perform a power method by reducing a number ofprocessing iterations and memory accesses required to perform the powermethod. The power method can be an iterative process for determining aproperty (e.g., a best rank-1 approximation) of a matrix. As an example,the electronic device can use a modified power method that requiresfewer processing iterations and fewer memory accesses to determine aparticular property of a matrix. This can result in less processingpower, memory, and electrical power being consumed by the electronicdevice to determine the particular property of the matrix.

A matrix can have various properties. One example of such a property isa rank. The rank of a matrix can be the smaller of (i) the number oflinearly independent rows in the matrix; or (ii) the number of linearlyindependent columns in the matrix. And if the matrix has any nonzerovalues, the matrix can at least have a rank of one. In some examples, arow (or column) of the matrix can be linearly dependent if the row (orcolumn) can be defined as a linear combination of the other rows. A rowof the matrix can be linearly independent if the row cannot be definedas a linear combination of the other rows.

As a particular example, the matrix X can have the following values:

$X = \begin{bmatrix}1 & 1 & 0 & 2 \\{- 1} & {- 1} & 0 & {- 2}\end{bmatrix}$Because the matrix X has nonzero values, the rank of matrix X is atleast one. All of the rows are linearly dependent on one another (e.g.,the first row is the inverse of the second row), so they do notcontribute to the rank. And all of the columns are linearly dependent onone another (e.g., the sum of the first, second, and third columnsequals the fourth column), so they also do not contribute to the rank.Because the rank of matrix X must have at least a rank of one, and thereare no linearly independent rows or columns, the rank of matrix X isone.

As another example, the matrix Y can have the following values:

$Y = \begin{bmatrix}1 & 2 & 1 \\{- 2} & {- 3} & 1 \\3 & 5 & 0\end{bmatrix}$Because matrix Y has nonzero values, the rank of the matrix Y is atleast one. And the first two rows are linearly independent, so the rankof the matrix is at least two. Because all three columns are linearlydependent (e.g., the first row is equal to the sum of the second row andthe third row), they do not contribute to the rank. So, the rank ofmatrix Y is two.

As shown in the example above, a matrix can have a rank that is greaterthan one. But various programs and mathematical operations may require amatrix that has a rank of one. To accommodate these programs andmathematical operations, the values of the original matrix can bemodified (e.g., zeroed out) until the resulting matrix has a rank ofone. This resulting matrix can be referred to as rank-1 approximation ofthe original matrix.

Different methods can be used to determine a rank-1 approximation of amatrix. Some methods can yield rank-1 approximations that are (i) moreaccurate (e.g., they have smaller approximation errors) than the rank-1approximations obtained using other methods, (ii) determined faster thanusing the other methods, or (iii) both of these. In some examples, abest rank-1 approximation of a matrix A can solve or optimize thefollowing equation:min_(λ,u,v:u) _(T) _(u=v) _(T) _(v=1) ∥A−λuv ^(T)∥_(F) ²  Equation 1:where A is the matrix A; λ is a largest singular value of the matrix A;u is a left singular value that corresponds to the largest singularvalue; and v is a right singular value that corresponds to the largestsingular value.

In some examples, the power method can be used to solve Equation 1 todetermine the best rank-1 approximation of the matrix A. The powermethod can be implemented according to Algorithm 1 defined below:

Input: A, v₀

Output: u_(i), v_(i), λ_(i)

-   -   1: Set i=0    -   2: repeat    -   3: Set i=i+1    -   4:

${{Compute}\mspace{14mu} u_{i}} = \frac{{Av}_{i - 1}}{{{Av}_{i - 1}}_{2}}$

-   -   5:

${{Compute}\mspace{14mu} v_{i}} = \frac{A^{T}u_{i}}{{{A^{T}u_{i}}}_{2}}$

-   -   6: Set λ₁=u_(i) ^(T)Av_(i)=∥A^(T)u_(i)∥₂    -   7: until a convergence criterion is satisfied        where A is the original matrix A; v₀ is an initial, right        singular value that is nonzero; λ_(i) is the largest singular        value of the matrix at interval i; u_(i) is the left singular        value at interval i; and v_(i) is the right singular value at        interval i. But Algorithm 1 may need to perform hundreds or        thousands of iterations to determine the values (e.g., optimal        values) for u_(i), v_(i), and λ_(i). This may result in a        significant amount of processing power, memory, and electrical        power being consumed.

Some examples of the present disclosure overcome one or more of theabovementioned issues by performing an enhanced version of the powermethod, which is discussed in greater detail below. The enhanced versionof the power method can reduce the number of processing iterations andmemory accesses required to determine the best rank-1 approximation of amatrix.

FIGS. 1-10 depict examples of systems and methods usable forimplementing an enhanced power method on an electronic device accordingto some aspects. For example, FIG. 1 is a block diagram of an example ofthe hardware components of a computing system according to some aspects.Data transmission network 100 is a specialized computer system that maybe used for processing large amounts of data where a large number ofcomputer processing cycles are required.

Data transmission network 100 may also include computing environment114. Computing environment 114 may be a specialized computer or othermachine that processes the data received within the data transmissionnetwork 100. The computing environment 114 may include one or more othersystems. For example, computing environment 114 may include a databasesystem 118 or a communications grid 120. The data transmission network100 can include one or more processors (e.g., distributed over one ormore networks or otherwise in communication with one another) that, insome examples, can collectively be referred to as a processor.

Data transmission network 100 also includes one or more network devices102. Network devices 102 may include client devices that can communicatewith computing environment 114. For example, network devices 102 maysend data to the computing environment 114 to be processed, may sendcommunications to the computing environment 114 to control differentaspects of the computing environment or the data it is processing, amongother reasons. Network devices 102 may interact with the computingenvironment 114 through a number of ways, such as, for example, over oneor more networks 108.

In some examples, network devices 102 may provide a large amount ofdata, either all at once or streaming over a period of time (e.g., usingevent stream processing (ESP)), to the computing environment 114 vianetworks 108. For example, the network devices 102 can transmitelectronic messages for implementing an enhanced power method, all atonce or streaming over a period of time, to the computing environment114 via networks 108.

The network devices 102 may include network computers, sensors,databases, or other devices that may transmit or otherwise provide datato computing environment 114. For example, network devices 102 mayinclude local area network devices, such as routers, hubs, switches, orother computer networking devices. These devices may provide a varietyof stored or generated data, such as network data or data specific tothe network devices 102 themselves. Network devices 102 may also includesensors that monitor their environment or other devices to collect dataregarding that environment or those devices, and such network devices102 may provide data they collect over time. Network devices 102 mayalso include devices within the internet of things, such as deviceswithin a home automation network. Some of these devices may be referredto as edge devices, and may involve edge-computing circuitry. Data maybe transmitted by network devices 102 directly to computing environment114 or to network-attached data stores, such as network-attached datastores 110 for storage so that the data may be retrieved later by thecomputing environment 114 or other portions of data transmission network100. For example, the network devices 102 can transmit data usable forimplementing an enhanced power method to a network-attached data store110 for storage. The computing environment 114 may later retrieve thedata from the network-attached data store 110 and use the data toimplement an enhanced power method.

Network-attached data stores 110 can store data to be processed by thecomputing environment 114 as well as any intermediate or final datagenerated by the computing system in non-volatile memory. But in certainexamples, the configuration of the computing environment 114 allows itsoperations to be performed such that intermediate and final data resultscan be stored solely in volatile memory (e.g., RAM), without arequirement that intermediate or final data results be stored tonon-volatile types of memory (e.g., disk). This can be useful in certainsituations, such as when the computing environment 114 receives ad hocqueries from a user and when responses, which are generated byprocessing large amounts of data, need to be generated dynamically(e.g., on the fly). In this situation, the computing environment 114 maybe configured to retain the processed information within memory so thatresponses can be generated for the user at different levels of detail aswell as allow a user to interactively query against this information.

Network-attached data stores 110 may store a variety of different typesof data organized in a variety of different ways and from a variety ofdifferent sources. For example, network-attached data stores may includestorage other than primary storage located within computing environment114 that is directly accessible by processors located therein.Network-attached data stores may include secondary, tertiary orauxiliary storage, such as large hard drives, servers, virtual memory,among other types. Storage devices may include portable or non-portablestorage devices, optical storage devices, and various other mediumscapable of storing, containing data. A machine-readable storage mediumor computer-readable storage medium may include a non-transitory mediumin which data can be stored and that does not include carrier waves ortransitory electronic communications. Examples of a non-transitorymedium may include, for example, a magnetic disk or tape, opticalstorage media such as compact disk or digital versatile disk, flashmemory, memory or memory devices. A computer-program product may includecode or machine-executable instructions that may represent a procedure,a function, a subprogram, a program, a routine, a subroutine, a module,a software package, a class, or any combination of instructions, datastructures, or program statements. A code segment may be coupled toanother code segment or a hardware circuit by passing or receivinginformation, data, arguments, parameters, or memory contents.Information, arguments, parameters, data, etc. may be passed, forwarded,or transmitted via any suitable means including memory sharing, messagepassing, token passing, network transmission, among others. Furthermore,the data stores may hold a variety of different types of data. Forexample, network-attached data stores 110 may hold unstructured (e.g.,raw) data.

The unstructured data may be presented to the computing environment 114in different forms such as a flat file or a conglomerate of datarecords, and may have data values and accompanying time stamps. Thecomputing environment 114 may be used to analyze the unstructured datain a variety of ways to determine the best way to structure (e.g.,hierarchically) that data, such that the structured data is tailored toa type of further analysis that a user wishes to perform on the data.For example, after being processed, the unstructured time-stamped datamay be aggregated by time (e.g., into daily time period units) orstructured hierarchically according to one or more dimensions (e.g.,parameters, attributes, or variables). For example, data may be storedin a hierarchical data structure, such as a relational online analyticalprocessing (ROLLUP) or multidimensional online analytical processing(MOLAR) database, or may be stored in another tabular form, such as in aflat-hierarchy form.

Data transmission network 100 may also include one or more server farms106. Computing environment 114 may route select communications or datato the sever farms 106 or one or more servers within the server farms106. Server farms 106 can be configured to provide information in apredetermined manner. For example, server farms 106 may access data totransmit in response to a communication. Server farms 106 may beseparately housed from each other device within data transmissionnetwork 100, such as computing environment 114, or may be part of adevice or system.

Server farms 106 may host a variety of different types of dataprocessing as part of data transmission network 100. Server farms 106may receive a variety of different data from network devices, fromcomputing environment 114, from cloud network 116, or from othersources. The data may have been obtained or collected from one or morewebsites, sensors, as inputs from a control database, or may have beenreceived as inputs from an external system or device. Server farms 106may assist in processing the data by turning raw data into processeddata based on one or more rules implemented by the server farms. Forexample, sensor data may be analyzed to determine changes in anenvironment over time or in real-time.

Data transmission network 100 may also include one or more cloudnetworks 116. Cloud network 116 may include a cloud infrastructuresystem that provides cloud services. In certain examples, servicesprovided by the cloud network 116 may include a host of services thatare made available to users of the cloud infrastructure system ondemand. Cloud network 116 is shown in FIG. 1 as being connected tocomputing environment 114 (and therefore having computing environment114 as its client or user), but cloud network 116 may be connected to orutilized by any of the devices in FIG. 1. Services provided by the cloudnetwork 116 can dynamically scale to meet the needs of its users. Thecloud network 116 may include one or more computers, servers, orsystems. In some examples, the computers, servers, or systems that makeup the cloud network 116 are different from the user's own on-premisescomputers, servers, or systems. For example, the cloud network 116 mayhost an application, and a user may, via a communication network such asthe Internet, order and use the application on demand. In some examples,the cloud network 116 may host an application for implementing anenhanced power method.

While each device, server, and system in FIG. 1 is shown as a singledevice, multiple devices may instead be used. For example, a set ofnetwork devices can be used to transmit various communications from asingle user, or remote server 140 may include a server stack. As anotherexample, data may be processed as part of computing environment 114.

Each communication within data transmission network 100 (e.g., betweenclient devices, between a device and connection management system 150,between server farms 106 and computing environment 114, or between aserver and a device) may occur over one or more networks 108. Networks108 may include one or more of a variety of different types of networks,including a wireless network, a wired network, or a combination of awired and wireless network. Examples of suitable networks include theInternet, a personal area network, a local area network (LAN), a widearea network (WAN), or a wireless local area network (WAN). A wirelessnetwork may include a wireless interface or combination of wirelessinterfaces. As an example, a network in the one or more networks 108 mayinclude a short-range communication channel, such as a Bluetooth or aBluetooth Low Energy channel. A wired network may include a wiredinterface. The wired or wireless networks may be implemented usingrouters, access points, bridges, gateways, or the like, to connectdevices in the network 108. The networks 108 can be incorporatedentirely within or can include an intranet, an extranet, or acombination thereof. In one example, communications between two or moresystems or devices can be achieved by a secure communications protocol,such as secure sockets layer (SEL) or transport layer security (TLS). Inaddition, data or transactional details may be encrypted.

Some aspects may utilize the Internet of Things (Iota), where things(e.g., machines, devices, phones, sensors) can be connected to networksand the data from these things can be collected and processed within thethings or external to the things. For example, the Iota can includesensors in many different devices, and high value analytics can beapplied to identify hidden relationships and drive increasedefficiencies. This can apply to both big data analytics and real-time(e.g., ESP) analytics.

As noted, computing environment 114 may include a communications grid120 and a transmission network database system 118. Communications grid120 may be a grid-based computing system for processing large amounts ofdata. The transmission network database system 118 may be for managing,storing, and retrieving large amounts of data that are distributed toand stored in the one or more network-attached data stores 110 or otherdata stores that reside at different locations within the transmissionnetwork database system 118. The computing nodes in the communicationsgrid 120 and the transmission network database system 118 may share thesame processor hardware, such as processors that are located withincomputing environment 114.

In some examples, the computing environment 114, a network device 102,or both can implement one or more processes for implementing an enhancedpower method. For example, the computing environment 114, a networkdevice 102, or both can implement one or more versions of the processesdiscussed with respect to FIGS. 11-12.

FIG. 2 is an example of devices that can communicate with each otherover an exchange system and via a network according to some aspects. Asnoted, each communication within data transmission network 100 may occurover one or more networks. System 200 includes a network device 204configured to communicate with a variety of types of client devices, forexample client devices 230, over a variety of types of communicationchannels.

As shown in FIG. 2, network device 204 can transmit a communication overa network (e.g., a cellular network via a base station 210). In someexamples, the communication can include times series data. Thecommunication can be routed to another network device, such as networkdevices 205-209, via base station 210. The communication can also berouted to computing environment 214 via base station 210. In someexamples, the network device 204 may collect data either from itssurrounding environment or from other network devices (such as networkdevices 205-209) and transmit that data to computing environment 214.

Although network devices 204-209 are shown in FIG. 2 as a mobile phone,laptop computer, tablet computer, temperature sensor, motion sensor, andaudio sensor respectively, the network devices may be or include sensorsthat are sensitive to detecting aspects of their environment. Forexample, the network devices may include sensors such as water sensors,power sensors, electrical current sensors, chemical sensors, opticalsensors, pressure sensors, geographic or position sensors (e.g., GPS),velocity sensors, acceleration sensors, flow rate sensors, among others.Examples of characteristics that may be sensed include force, torque,load, strain, position, temperature, air pressure, fluid flow, chemicalproperties, resistance, electromagnetic fields, radiation, irradiance,proximity, acoustics, moisture, distance, speed, vibrations,acceleration, electrical potential, and electrical current, amongothers. The sensors may be mounted to various components used as part ofa variety of different types of systems. The network devices may detectand record data related to the environment that it monitors, andtransmit that data to computing environment 214.

The network devices 204-209 may also perform processing on data itcollects before transmitting the data to the computing environment 214,or before deciding whether to transmit data to the computing environment214. For example, network devices 204-209 may determine whether datacollected meets certain rules, for example by comparing data or valuescalculated from the data and comparing that data to one or morethresholds. The network devices 204-209 may use this data or comparisonsto determine if the data is to be transmitted to the computingenvironment 214 for further use or processing. In some examples, thenetwork devices 204-209 can pre-process the data prior to transmittingthe data to the computing environment 214. For example, the networkdevices 204-209 can reformat the data before transmitting the data tothe computing environment 214 for further processing (e.g., implementingan enhanced power method).

Computing environment 214 may include machines 220, 240. Althoughcomputing environment 214 is shown in FIG. 2 as having two machines 220,240, computing environment 214 may have only one machine or may havemore than two machines. The machines 220, 240 that make up computingenvironment 214 may include specialized computers, servers, or othermachines that are configured to individually or collectively processlarge amounts of data. The computing environment 214 may also includestorage devices that include one or more databases of structured data,such as data organized in one or more hierarchies, or unstructured data.The databases may communicate with the processing devices withincomputing environment 214 to distribute data to them. Since networkdevices may transmit data to computing environment 214, that data may bereceived by the computing environment 214 and subsequently stored withinthose storage devices. Data used by computing environment 214 may alsobe stored in data stores 235, which may also be a part of or connectedto computing environment 214.

Computing environment 214 can communicate with various devices via oneor more routers 225 or other inter-network or intra-network connectioncomponents. For example, computing environment 214 may communicate withclient devices 230 via one or more routers 225. Computing environment214 may collect, analyze or store data from or pertaining tocommunications, client device operations, client rules, oruser-associated actions stored at one or more data stores 235. Such datamay influence communication routing to the devices within computingenvironment 214, how data is stored or processed within computingenvironment 214, among other actions.

Notably, various other devices can further be used to influencecommunication routing or processing between devices within computingenvironment 214 and with devices outside of computing environment 214.For example, as shown in FIG. 2, computing environment 214 may include amachine 240 that is a web server. Computing environment 214 can retrievedata of interest, such as client information (e.g., product information,client rules, etc.), technical product details, news, blog posts,e-mails, forum posts, electronic documents, social media posts (e.g.,Twitter™ posts or Facebook™ posts), time series data, and so on.

In addition to computing environment 214 collecting data (e.g., asreceived from network devices, such as sensors, and client devices orother sources) to be processed as part of a big data analytics project,it may also receive data in real time as part of a streaming analyticsenvironment. As noted, data may be collected using a variety of sourcesas communicated via different kinds of networks or locally. Such datamay be received on a real-time streaming basis. For example, networkdevices 204-209 may receive data periodically and in real time from aweb server or other source. Devices within computing environment 214 mayalso perform pre-analysis on data it receives to determine if the datareceived should be processed as part of an ongoing project. For example,as part of a project in which an enhanced power method is to beimplemented, the computing environment 214 can perform a pre-analysis ofthe data. The pre-analysis can include determining whether the data isin a correct format for performing an enhanced power method using thedata and, if not, reformatting the data into the correct format.

FIG. 3 is a block diagram of a model of an example of a communicationsprotocol system according to some aspects. More specifically, FIG. 3identifies operation of a computing environment in an Open SystemsInteraction model that corresponds to various connection components. Themodel 300 shows, for example, how a computing environment, such ascomputing environment (or computing environment 214 in FIG. 2) maycommunicate with other devices in its network, and control howcommunications between the computing environment and other devices areexecuted and under what conditions.

The model 300 can include layers 302-314. The layers 302-314 arearranged in a stack. Each layer in the stack serves the layer one levelhigher than it (except for the application layer, which is the highestlayer), and is served by the layer one level below it (except for thephysical layer 302, which is the lowest layer). The physical layer 302is the lowest layer because it receives and transmits raw bites of data,and is the farthest layer from the user in a communications system. Onthe other hand, the application layer is the highest layer because itinteracts directly with a software application.

As noted, the model 300 includes a physical layer 302. Physical layer302 represents physical communication, and can define parameters of thatphysical communication. For example, such physical communication maycome in the form of electrical, optical, or electromagneticcommunications. Physical layer 302 also defines protocols that maycontrol communications within a data transmission network.

Link layer 304 defines links and mechanisms used to transmit (e.g.,move) data across a network. The link layer manages node-to-nodecommunications, such as within a grid-computing environment. Link layer304 can detect and correct errors (e.g., transmission errors in thephysical layer 302). Link layer 304 can also include a media accesscontrol (MAC) layer and logical link control (LLC) layer.

Network layer 306 can define the protocol for routing within a network.In other words, the network layer coordinates transferring data acrossnodes in a same network (e.g., such as a grid-computing environment).Network layer 306 can also define the processes used to structure localaddressing within the network.

Transport layer 308 can manage the transmission of data and the qualityof the transmission or receipt of that data. Transport layer 308 canprovide a protocol for transferring data, such as, for example, aTransmission Control Protocol (TCP). Transport layer 308 can assembleand disassemble data frames for transmission. The transport layer canalso detect transmission errors occurring in the layers below it.

Session layer 310 can establish, maintain, and manage communicationconnections between devices on a network. In other words, the sessionlayer controls the dialogues or nature of communications between networkdevices on the network. The session layer may also establish checkpointing, adjournment, termination, and restart procedures.

Presentation layer 312 can provide translation for communicationsbetween the application and network layers. In other words, this layermay encrypt, decrypt or format data based on data types known to beaccepted by an application or network layer.

Application layer 314 interacts directly with software applications andend users, and manages communications between them. Application layer314 can identify destinations, local resource states or availability orcommunication content or formatting using the applications.

For example, a communication link can be established between two deviceson a network. One device can transmit an analog or digitalrepresentation of an electronic message that includes a data set to theother device. The other device can receive the analog or digitalrepresentation at the physical layer 302. The other device can transmitthe data associated with the electronic message through the remaininglayers 304-314. The application layer 314 can receive data associatedwith the electronic message. The application layer 314 can identify oneor more applications, such as an application for implementing anenhanced power method, to which to transmit data associated with theelectronic message. The application layer 314 can transmit the data tothe identified application.

Intra-network connection components 322, 324 can operate in lowerlevels, such as physical layer 302 and link layer 304, respectively. Forexample, a hub can operate in the physical layer, a switch can operatein the physical layer, and a router can operate in the network layer.Inter-network connection components 326, 328 are shown to operate onhigher levels, such as layers 306-314. For example, routers can operatein the network layer and network devices can operate in the transport,session, presentation, and application layers.

A computing environment 330 can interact with or operate on, in variousexamples, one, more, all or any of the various layers. For example,computing environment 330 can interact with a hub (e.g., via the linklayer) to adjust which devices the hub communicates with. The physicallayer 302 may be served by the link layer 304, so it may implement suchdata from the link layer 304. For example, the computing environment 330may control which devices from which it can receive data. For example,if the computing environment 330 knows that a certain network device hasturned off, broken, or otherwise become unavailable or unreliable, thecomputing environment 330 may instruct the hub to prevent any data frombeing transmitted to the computing environment 330 from that networkdevice. Such a process may be beneficial to avoid receiving data that isinaccurate or that has been influenced by an uncontrolled environment.As another example, computing environment 330 can communicate with abridge, switch, router or gateway and influence which device within thesystem (e.g., system 200) the component selects as a destination. Insome examples, computing environment 330 can interact with variouslayers by exchanging communications with equipment operating on aparticular layer by routing or modifying existing communications. Inanother example, such as in a grid-computing environment, a node maydetermine how data within the environment should be routed (e.g., whichnode should receive certain data) based on certain parameters orinformation provided by other layers within the model.

The computing environment 330 may be a part of a communications gridenvironment, the communications of which may be implemented as shown inthe protocol of FIG. 3. For example, referring back to FIG. 2, one ormore of machines 220 and 240 may be part of a communicationsgrid-computing environment. A gridded computing environment may beemployed in a distributed system with non-interactive workloads wheredata resides in memory on the machines, or compute nodes. In such anenvironment, analytic code, instead of a database management system, cancontrol the processing performed by the nodes. Data is co-located bypre-distributing it to the grid nodes, and the analytic code on eachnode loads the local data into memory. Each node may be assigned aparticular task, such as a portion of a processing project, or toorganize or control other nodes within the grid. For example, each nodemay be assigned a portion of a processing task for implementing anenhanced power method.

FIG. 4 is a hierarchical diagram of an example of a communications gridcomputing system 400 including a variety of control and worker nodesaccording to some aspects. Communications grid computing system 400includes three control nodes and one or more worker nodes.Communications grid computing system 400 includes control nodes 402,404, and 406. The control nodes are communicatively connected viacommunication paths 451, 453, and 455. The control nodes 402-406 maytransmit information (e.g., related to the communications grid ornotifications) to and receive information from each other. Althoughcommunications grid computing system 400 is shown in FIG. 4 as includingthree control nodes, the communications grid may include more or lessthan three control nodes.

Communications grid computing system 400 (which can be referred to as a“communications grid”) also includes one or more worker nodes. Shown inFIG. 4 are six worker nodes 410-420. Although FIG. 4 shows six workernodes, a communications grid can include more or less than six workernodes. The number of worker nodes included in a communications grid maybe dependent upon how large the project or data set is being processedby the communications grid, the capacity of each worker node, the timedesignated for the communications grid to complete the project, amongothers. Each worker node within the communications grid computing system400 may be connected (wired or wirelessly, and directly or indirectly)to control nodes 402-406. Each worker node may receive information fromthe control nodes (e.g., an instruction to perform work on a project)and may transmit information to the control nodes (e.g., a result fromwork performed on a project). Furthermore, worker nodes may communicatewith each other directly or indirectly. For example, worker nodes maytransmit data between each other related to a job being performed or anindividual task within a job being performed by that worker node. Insome examples, worker nodes may not be connected (communicatively orotherwise) to certain other worker nodes. For example, a worker node 410may only be able to communicate with a particular control node 402. Theworker node 410 may be unable to communicate with other worker nodes412-420 in the communications grid, even if the other worker nodes412-420 are controlled by the same control node 402.

A control node 402-406 may connect with an external device with whichthe control node 402-406 may communicate (e.g., a communications griduser, such as a server or computer, may connect to a controller of thegrid). For example, a server or computer may connect to control nodes402-406 and may transmit a project or job to the node, such as a projector job related to (or including) implementing an enhanced power method.The project may include a data set. The data set may be of any size.Once the control node 402-406 receives such a project including a largedata set, the control node may distribute the data set or projectsrelated to the data set to be performed by worker nodes. Alternatively,for a project including a large data set, the data set may be receive orstored by a machine other than a control node 402-406 (e.g., a Hadoopdata node).

Control nodes 402-406 can maintain knowledge of the status of the nodesin the grid (e.g., grid status information), accept work requests fromclients, subdivide the work across worker nodes, and coordinate theworker nodes, among other responsibilities. Worker nodes 412-420 mayaccept work requests from a control node 402-406 and provide the controlnode with results of the work performed by the worker node. A grid maybe started from a single node (e.g., a machine, computer, server, etc.).This first node may be assigned or may start as the primary control node402 that will control any additional nodes that enter the grid.

When a project is submitted for execution (e.g., by a client or acontroller of the grid) it may be assigned to a set of nodes. After thenodes are assigned to a project, a data structure (e.g., a communicator)may be created. The communicator may be used by the project forinformation to be shared between the project code running on each node.A communication handle may be created on each node. A handle, forexample, is a reference to the communicator that is valid within asingle process on a single node, and the handle may be used whenrequesting communications between nodes.

A control node, such as control node 402, may be designated as theprimary control node. A server, computer or other external device mayconnect to the primary control node. Once the control node 402 receivesa project, the primary control node may distribute portions of theproject to its worker nodes for execution. For example, a project forpredicting future interest in an object can be initiated oncommunications grid computing system 400. A primary control node cancontrol the work to be performed for the project in order to completethe project as requested or instructed. The primary control node maydistribute work to the worker nodes 412-420 based on various factors,such as which subsets or portions of projects may be completed mostefficiently and in the correct amount of time. For example, a workernode 412 may perform an enhanced power method using at least a portionof data that is already local (e.g., stored on) the worker node. Theprimary control node also coordinates and processes the results of thework performed by each worker node 412-420 after each worker node412-420 executes and completes its job. For example, the primary controlnode may receive a result from one or more worker nodes 412-420, and theprimary control node may organize (e.g., collect and assemble) theresults received and compile them to produce a complete result for theproject received from the end user.

Any remaining control nodes, such as control nodes 404, 406, may beassigned as backup control nodes for the project. In an example, backupcontrol nodes may not control any portion of the project. Instead,backup control nodes may serve as a backup for the primary control nodeand take over as primary control node if the primary control node wereto fail. If a communications grid were to include only a single controlnode 402, and the control node 402 were to fail (e.g., the control nodeis shut off or breaks) then the communications grid as a whole may failand any project or job being run on the communications grid may fail andmay not complete. While the project may be run again, such a failure maycause a delay (severe delay in some cases, such as overnight delay) incompletion of the project. Therefore, a grid with multiple control nodes402-406, including a backup control node, may be beneficial.

In some examples, the primary control node may open a pair of listeningsockets to add another node or machine to the grid. A socket may be usedto accept work requests from clients, and the second socket may be usedto accept connections from other grid nodes. The primary control nodemay be provided with a list of other nodes (e.g., other machines,computers, servers, etc.) that can participate in the grid, and the rolethat each node can fill in the grid. Upon startup of the primary controlnode (e.g., the first node on the grid), the primary control node mayuse a network protocol to start the server process on every other nodein the grid. Command line parameters, for example, may inform each nodeof one or more pieces of information, such as: the role that the nodewill have in the grid, the host name of the primary control node, theport number on which the primary control node is accepting connectionsfrom peer nodes, among others. The information may also be provided in aconfiguration file, transmitted over a secure shell tunnel, recoveredfrom a configuration server, among others. While the other machines inthe grid may not initially know about the configuration of the grid,that information may also be sent to each other node by the primarycontrol node. Updates of the grid information may also be subsequentlysent to those nodes.

For any control node other than the primary control node added to thegrid, the control node may open three sockets. The first socket mayaccept work requests from clients, the second socket may acceptconnections from other grid members, and the third socket may connect(e.g., permanently) to the primary control node. When a control node(e.g., primary control node) receives a connection from another controlnode, it first checks to see if the peer node is in the list ofconfigured nodes in the grid. If it is not on the list, the control nodemay clear the connection. If it is on the list, it may then attempt toauthenticate the connection. If authentication is successful, theauthenticating node may transmit information to its peer, such as theport number on which a node is listening for connections, the host nameof the node, information about how to authenticate the node, among otherinformation. When a node, such as the new control node, receivesinformation about another active node, it can check to see if it alreadyhas a connection to that other node. If it does not have a connection tothat node, it may then establish a connection to that control node.

Any worker node added to the grid may establish a connection to theprimary control node and any other control nodes on the grid. Afterestablishing the connection, it may authenticate itself to the grid(e.g., any control nodes, including both primary and backup, or a serveror user controlling the grid). After successful authentication, theworker node may accept configuration information from the control node.

When a node joins a communications grid (e.g., when the node is poweredon or connected to an existing node on the grid or both), the node isassigned (e.g., by an operating system of the grid) a universally uniqueidentifier (UUID). This unique identifier may help other nodes andexternal entities (devices, users, etc.) to identify the node anddistinguish it from other nodes. When a node is connected to the grid,the node may share its unique identifier with the other nodes in thegrid. Since each node may share its unique identifier, each node mayknow the unique identifier of every other node on the grid. Uniqueidentifiers may also designate a hierarchy of each of the nodes (e.g.,backup control nodes) within the grid. For example, the uniqueidentifiers of each of the backup control nodes may be stored in a listof backup control nodes to indicate an order in which the backup controlnodes will take over for a failed primary control node to become a newprimary control node. But, a hierarchy of nodes may also be determinedusing methods other than using the unique identifiers of the nodes. Forexample, the hierarchy may be predetermined, or may be assigned based onother predetermined factors.

The grid may add new machines at any time (e.g., initiated from anycontrol node). Upon adding a new node to the grid, the control node mayfirst add the new node to its table of grid nodes. The control node mayalso then notify every other control node about the new node. The nodesreceiving the notification may acknowledge that they have updated theirconfiguration information.

Primary control node 402 may, for example, transmit one or morecommunications to backup control nodes 404, 406 (and, for example, toother control or worker nodes 412-420 within the communications grid).Such communications may be sent periodically, at fixed time intervals,between known fixed stages of the project's execution, among otherprotocols. The communications transmitted by primary control node 402may be of varied types and may include a variety of types ofinformation. For example, primary control node 402 may transmitsnapshots (e.g., status information) of the communications grid so thatbackup control node 404 always has a recent snapshot of thecommunications grid. The snapshot or grid status may include, forexample, the structure of the grid (including, for example, the workernodes 410-420 in the communications grid, unique identifiers of theworker nodes 410-420, or their relationships with the primary controlnode 402) and the status of a project (including, for example, thestatus of each worker node's portion of the project). The snapshot mayalso include analysis or results received from worker nodes 410-420 inthe communications grid. The backup control nodes 404, 406 may receiveand store the backup data received from the primary control node 402.The backup control nodes 404, 406 may transmit a request for such asnapshot (or other information) from the primary control node 402, orthe primary control node 402 may send such information periodically tothe backup control nodes 404, 406.

As noted, the backup data may allow a backup control node 404, 406 totake over as primary control node if the primary control node 402 failswithout requiring the communications grid to start the project over fromscratch. If the primary control node 402 fails, the backup control node404, 406 that will take over as primary control node may retrieve themost recent version of the snapshot received from the primary controlnode 402 and use the snapshot to continue the project from the stage ofthe project indicated by the backup data. This may prevent failure ofthe project as a whole.

A backup control node 404, 406 may use various methods to determine thatthe primary control node 402 has failed. In one example of such amethod, the primary control node 402 may transmit (e.g., periodically) acommunication to the backup control node 404, 406 that indicates thatthe primary control node 402 is working and has not failed, such as aheartbeat communication. The backup control node 404, 406 may determinethat the primary control node 402 has failed if the backup control nodehas not received a heartbeat communication for a certain predeterminedperiod of time. Alternatively, a backup control node 404, 406 may alsoreceive a communication from the primary control node 402 itself (beforeit failed) or from a worker node 410-420 that the primary control node402 has failed, for example because the primary control node 402 hasfailed to communicate with the worker node 410-420.

Different methods may be performed to determine which backup controlnode of a set of backup control nodes (e.g., backup control nodes 404,406) can take over for failed primary control node 402 and become thenew primary control node. For example, the new primary control node maybe chosen based on a ranking or “hierarchy” of backup control nodesbased on their unique identifiers. In an alternative example, a backupcontrol node may be assigned to be the new primary control node byanother device in the communications grid or from an external device(e.g., a system infrastructure or an end user, such as a server orcomputer, controlling the communications grid). In another alternativeexample, the backup control node that takes over as the new primarycontrol node may be designated based on bandwidth or other statisticsabout the communications grid.

A worker node within the communications grid may also fail. If a workernode fails, work being performed by the failed worker node may beredistributed amongst the operational worker nodes. In an alternativeexample, the primary control node may transmit a communication to eachof the operable worker nodes still on the communications grid that eachof the worker nodes should purposefully fail also. After each of theworker nodes fail, they may each retrieve their most recent savedcheckpoint of their status and re-start the project from that checkpointto minimize lost progress on the project being executed. In someexamples, a communications grid computing system 400 can be used toperform an enhanced power method.

FIG. 5 is a flow chart of an example of a process for adjusting acommunications grid or a work project in a communications grid after afailure of a node according to some aspects. The process may include,for example, receiving grid status information including a projectstatus of a portion of a project being executed by a node in thecommunications grid, as described in operation 502. For example, acontrol node (e.g., a backup control node connected to a primary controlnode and a worker node on a communications grid) may receive grid statusinformation, where the grid status information includes a project statusof the primary control node or a project status of the worker node. Theproject status of the primary control node and the project status of theworker node may include a status of one or more portions of a projectbeing executed by the primary and worker nodes in the communicationsgrid. The process may also include storing the grid status information,as described in operation 504. For example, a control node (e.g., abackup control node) may store the received grid status informationlocally within the control node. Alternatively, the grid statusinformation may be sent to another device for storage where the controlnode may have access to the information.

The process may also include receiving a failure communicationcorresponding to a node in the communications grid in operation 506. Forexample, a node may receive a failure communication including anindication that the primary control node has failed, prompting a backupcontrol node to take over for the primary control node. In analternative embodiment, a node may receive a failure that a worker nodehas failed, prompting a control node to reassign the work beingperformed by the worker node. The process may also include reassigning anode or a portion of the project being executed by the failed node, asdescribed in operation 508. For example, a control node may designatethe backup control node as a new primary control node based on thefailure communication upon receiving the failure communication. If thefailed node is a worker node, a control node may identify a projectstatus of the failed worker node using the snapshot of thecommunications grid, where the project status of the failed worker nodeincludes a status of a portion of the project being executed by thefailed worker node at the failure time.

The process may also include receiving updated grid status informationbased on the reassignment, as described in operation 510, andtransmitting a set of instructions based on the updated grid statusinformation to one or more nodes in the communications grid, asdescribed in operation 512. The updated grid status information mayinclude an updated project status of the primary control node or anupdated project status of the worker node. The updated information maybe transmitted to the other nodes in the grid to update their stalestored information.

FIG. 6 is a block diagram of a portion of a communications gridcomputing system 600 including a control node and a worker nodeaccording to some aspects. Communications grid 600 computing systemincludes one control node (control node 602) and one worker node (workernode 610) for purposes of illustration, but may include more workerand/or control nodes. The control node 602 is communicatively connectedto worker node 610 via communication path 650. Therefore, control node602 may transmit information (e.g., related to the communications gridor notifications), to and receive information from worker node 610 viacommunication path 650.

Similar to in FIG. 4, communications grid computing system (or just“communications grid”) 600 includes data processing nodes (control node602 and worker node 610). Nodes 602 and 610 comprise multi-core dataprocessors. Each node 602 and 610 includes a grid-enabled softwarecomponent (GESC) 620 that executes on the data processor associated withthat node and interfaces with buffer memory 622 also associated withthat node. Each node 602 and 610 includes a database management software(DBMS) 628 that executes on a database server (not shown) at controlnode 602 and on a database server (not shown) at worker node 610.

Each node also includes a data store 624. Data stores 624, similar tonetwork-attached data stores 110 in FIG. 1 and data stores 235 in FIG.2, are used to store data to be processed by the nodes in the computingenvironment. Data stores 624 may also store any intermediate or finaldata generated by the computing system after being processed, forexample in non-volatile memory. However in certain examples, theconfiguration of the grid computing environment allows its operations tobe performed such that intermediate and final data results can be storedsolely in volatile memory (e.g., RAM), without a requirement thatintermediate or final data results be stored to non-volatile types ofmemory. Storing such data in volatile memory may be useful in certainsituations, such as when the grid receives queries (e.g., ad hoc) from aclient and when responses, which are generated by processing largeamounts of data, need to be generated quickly or on-the-fly. In such asituation, the grid may be configured to retain the data within memoryso that responses can be generated at different levels of detail and sothat a client may interactively query against this information.

Each node also includes a user-defined function (UDF) 626. The UDFprovides a mechanism for the DMBS 628 to transfer data to or receivedata from the database stored in the data stores 624 that are managed bythe DBMS. For example, UDF 626 can be invoked by the DBMS to providedata to the GESC for processing. The UDF 626 may establish a socketconnection (not shown) with the GESC to transfer the data.Alternatively, the UDF 626 can transfer data to the GESC by writing datato shared memory accessible by both the UDF and the GESC.

The GESC 620 at the nodes 602 and 610 may be connected via a network,such as network 108 shown in FIG. 1. Therefore, nodes 602 and 610 cancommunicate with each other via the network using a predeterminedcommunication protocol such as, for example, the Message PassingInterface (MPI). Each GESC 620 can engage in point-to-pointcommunication with the GESC at another node or in collectivecommunication with multiple GESCs via the network. The GESC 620 at eachnode may contain identical (or nearly identical) software instructions.Each node may be capable of operating as either a control node or aworker node. The GESC at the control node 602 can communicate, over acommunication path 652, with a client device 630. More specifically,control node 602 may communicate with client application 632 hosted bythe client device 630 to receive queries and to respond to those queriesafter processing large amounts of data.

DMBS 628 may control the creation, maintenance, and use of database ordata structure (not shown) within nodes 602 or 610. The database mayorganize data stored in data stores 624. The DMBS 628 at control node602 may accept requests for data and transfer the appropriate data forthe request. With such a process, collections of data may be distributedacross multiple physical locations. In this example, each node 602 and610 stores a portion of the total data managed by the management systemin its associated data store 624.

Furthermore, the DBMS may be responsible for protecting against dataloss using replication techniques. Replication includes providing abackup copy of data stored on one node on one or more other nodes.Therefore, if one node fails, the data from the failed node can berecovered from a replicated copy residing at another node. However, asdescribed herein with respect to FIG. 4, data or status information foreach node in the communications grid may also be shared with each nodeon the grid.

FIG. 7 is a flow chart of an example of a process for executing a dataanalysis or a processing project according to some aspects. As describedwith respect to FIG. 6, the GESC at the control node may transmit datawith a client device (e.g., client device 630) to receive queries forexecuting a project and to respond to those queries after large amountsof data have been processed. The query may be transmitted to the controlnode, where the query may include a request for executing a project, asdescribed in operation 702. The query can contain instructions on thetype of data analysis to be performed in the project and whether theproject should be executed using the grid-based computing environment,as shown in operation 704.

To initiate the project, the control node may determine if the queryrequests use of the grid-based computing environment to execute theproject. If the determination is no, then the control node initiatesexecution of the project in a solo environment (e.g., at the controlnode), as described in operation 710. If the determination is yes, thecontrol node may initiate execution of the project in the grid-basedcomputing environment, as described in operation 706. In such asituation, the request may include a requested configuration of thegrid. For example, the request may include a number of control nodes anda number of worker nodes to be used in the grid when executing theproject. After the project has been completed, the control node maytransmit results of the analysis yielded by the grid, as described inoperation 708. Whether the project is executed in a solo or grid-basedenvironment, the control node provides the results of the project.

As noted with respect to FIG. 2, the computing environments describedherein may collect data (e.g., as received from network devices, such assensors, such as network devices 204-209 in FIG. 2, and client devicesor other sources) to be processed as part of a data analytics project,and data may be received in real time as part of a streaming analyticsenvironment (e.g., ESP). Data may be collected using a variety ofsources as communicated via different kinds of networks or locally, suchas on a real-time streaming basis. For example, network devices mayreceive data periodically from network device sensors as the sensorscontinuously sense, monitor and track changes in their environments.More specifically, an increasing number of distributed applicationsdevelop or produce continuously flowing data from distributed sources byapplying queries to the data before distributing the data togeographically distributed recipients. An event stream processing engine(ESPE) may continuously apply the queries to the data as it is receivedand determines which entities should receive the data. Client or otherdevices may also subscribe to the ESPE or other devices processing ESPdata so that they can receive data after processing, based on forexample the entities determined by the processing engine. For example,client devices 230 in FIG. 2 may subscribe to the ESPE in computingenvironment 214. In another example, event subscription devices 1024a-c, described further with respect to FIG. 10, may also subscribe tothe ESPE. The ESPE may determine or define how input data or eventstreams from network devices or other publishers (e.g., network devices204-209 in FIG. 2) are transformed into meaningful output data to beconsumed by subscribers, such as for example client devices 230 in FIG.2.

FIG. 8 is a block diagram including components of an Event StreamProcessing Engine (ESPE) according to some aspects. ESPE 800 may includeone or more projects 802. A project may be described as a second-levelcontainer in an engine model managed by ESPE 800 where a thread poolsize for the project may be defined by a user. Each project of the oneor more projects 802 may include one or more continuous queries 804 thatcontain data flows, which are data transformations of incoming eventstreams. The one or more continuous queries 804 may include one or moresource windows 806 and one or more derived windows 808.

The ESPE may receive streaming data over a period of time related tocertain events, such as events or other data sensed by one or morenetwork devices. The ESPE may perform operations associated withprocessing data created by the one or more devices. For example, theESPE may receive data from the one or more network devices 204-209 shownin FIG. 2. As noted, the network devices may include sensors that sensedifferent aspects of their environments, and may collect data over timebased on those sensed observations. For example, the ESPE may beimplemented within one or more of machines 220 and 240 shown in FIG. 2.The ESPE may be implemented within such a machine by an ESP application.An ESP application may embed an ESPE with its own dedicated thread poolor pools into its application space where the main application threadcan do application-specific work and the ESPE processes event streams atleast by creating an instance of a model into processing objects.

The engine container is the top-level container in a model that managesthe resources of the one or more projects 802. In an illustrativeexample, there may be only one ESPE 800 for each instance of the ESPapplication, and ESPE 800 may have a unique engine name. Additionally,the one or more projects 802 may each have unique project names, andeach query may have a unique continuous query name and begin with auniquely named source window of the one or more source windows 806. ESPE800 may or may not be persistent.

Continuous query modeling involves defining directed graphs of windowsfor event stream manipulation and transformation. A window in thecontext of event stream manipulation and transformation is a processingnode in an event stream processing model. A window in a continuous querycan perform aggregations, computations, pattern-matching, and otheroperations on data flowing through the window. A continuous query may bedescribed as a directed graph of source, relational, pattern matching,and procedural windows. The one or more source windows 806 and the oneor more derived windows 808 represent continuously executing queriesthat generate updates to a query result set as new event blocks streamthrough ESPE 800. A directed graph, for example, is a set of nodesconnected by edges, where the edges have a direction associated withthem.

An event object may be described as a packet of data accessible as acollection of fields, with at least one of the fields defined as a keyor unique identifier (ID). The event object may be created using avariety of formats including binary, alphanumeric, XML, etc. Each eventobject may include one or more fields designated as a primary identifier(ID) for the event so ESPE 800 can support operation codes (opcodes) forevents including insert, update, upsert, and delete. Upsert opcodesupdate the event if the key field already exists; otherwise, the eventis inserted. For illustration, an event object may be a packed binaryrepresentation of a set of field values and include both metadata andfield data associated with an event. The metadata may include an opcodeindicating if the event represents an insert, update, delete, or upsert,a set of flags indicating if the event is a normal, partial-update, or aretention generated event from retention policy management, and a set ofmicrosecond timestamps that can be used for latency measurements.

An event block object may be described as a grouping or package of eventobjects. An event stream may be described as a flow of event blockobjects. A continuous query of the one or more continuous queries 804transforms a source event stream made up of streaming event blockobjects published into ESPE 800 into one or more output event streamsusing the one or more source windows 806 and the one or more derivedwindows 808. A continuous query can also be thought of as data flowmodeling.

The one or more source windows 806 are at the top of the directed graphand have no windows feeding into them. Event streams are published intothe one or more source windows 806, and from there, the event streamsmay be directed to the next set of connected windows as defined by thedirected graph. The one or more derived windows 808 are all instantiatedwindows that are not source windows and that have other windowsstreaming events into them. The one or more derived windows 808 mayperform computations or transformations on the incoming event streams.The one or more derived windows 808 transform event streams based on thewindow type (that is operators such as join, filter, compute, aggregate,copy, pattern match, procedural, union, etc.) and window settings. Asevent streams are published into ESPE 800, they are continuouslyqueried, and the resulting sets of derived windows in these queries arecontinuously updated.

FIG. 9 is a flow chart of an example of a process including operationsperformed by an event stream processing engine according to someaspects. As noted, the ESPE 800 (or an associated ESP application)defines how input event streams are transformed into meaningful outputevent streams. More specifically, the ESP application may define howinput event streams from publishers (e.g., network devices providingsensed data) are transformed into meaningful output event streamsconsumed by subscribers (e.g., a data analytics project being executedby a machine or set of machines).

Within the application, a user may interact with one or more userinterface windows presented to the user in a display under control ofthe ESPE independently or through a browser application in an orderselectable by the user. For example, a user may execute an ESPapplication, which causes presentation of a first user interface window,which may include a plurality of menus and selectors such as drop downmenus, buttons, text boxes, hyperlinks, etc. associated with the ESPapplication as understood by a person of skill in the art. Variousoperations may be performed in parallel, for example, using a pluralityof threads.

At operation 900, an ESP application may define and start an ESPE,thereby instantiating an ESPE at a device, such as machine 220 and/or240. In an operation 902, the engine container is created. Forillustration, ESPE 800 may be instantiated using a function call thatspecifies the engine container as a manager for the model.

In an operation 904, the one or more continuous queries 804 areinstantiated by ESPE 800 as a model. The one or more continuous queries804 may be instantiated with a dedicated thread pool or pools thatgenerate updates as new events stream through ESPE 800. Forillustration, the one or more continuous queries 804 may be created tomodel business processing logic within ESPE 800, to predict eventswithin ESPE 800, to model a physical system within ESPE 800, to predictthe physical system state within ESPE 800, etc. For example, as noted,ESPE 800 may be used to support sensor data monitoring and management(e.g., sensing may include force, torque, load, strain, position,temperature, air pressure, fluid flow, chemical properties, resistance,electromagnetic fields, radiation, irradiance, proximity, acoustics,moisture, distance, speed, vibrations, acceleration, electricalpotential, or electrical current, etc.).

ESPE 800 may analyze and process events in motion or “event streams.”Instead of storing data and running queries against the stored data,ESPE 800 may store queries and stream data through them to allowcontinuous analysis of data as it is received. The one or more sourcewindows 806 and the one or more derived windows 808 may be created basedon the relational, pattern matching, and procedural algorithms thattransform the input event streams into the output event streams tomodel, simulate, score, test, predict, etc. based on the continuousquery model defined and application to the streamed data.

In an operation 906, a publish/subscribe (pub/sub) capability isinitialized for ESPE 800. In an illustrative embodiment, a pub/subcapability is initialized for each project of the one or more projects802. To initialize and enable pub/sub capability for ESPE 800, a portnumber may be provided. Pub/sub clients can use a host name of an ESPdevice running the ESPE and the port number to establish pub/subconnections to ESPE 800.

FIG. 10 is a block diagram of an ESP system 1000 interfacing betweenpublishing device 1022 and event subscribing devices 1024 a-c accordingto some aspects. ESP system 1000 may include ESP device or subsystem1001, publishing device 1022, an event subscribing device A 1024 a, anevent subscribing device B 1024 b, and an event subscribing device C1024 c. Input event streams are output to ESP device 1001 by publishingdevice 1022. In alternative embodiments, the input event streams may becreated by a plurality of publishing devices. The plurality ofpublishing devices further may publish event streams to other ESPdevices. The one or more continuous queries instantiated by ESPE 800 mayanalyze and process the input event streams to form output event streamsoutput to event subscribing device A 1024 a, event subscribing device B1024 b, and event subscribing device C 1024 c. ESP system 1000 mayinclude a greater or a fewer number of event subscribing devices ofevent subscribing devices.

Publish-subscribe is a message-oriented interaction paradigm based onindirect addressing. Processed data recipients specify their interest inreceiving information from ESPE 800 by subscribing to specific classesof events, while information sources publish events to ESPE 800 withoutdirectly addressing the receiving parties. ESPE 800 coordinates theinteractions and processes the data. In some cases, the data sourcereceives confirmation that the published information has been receivedby a data recipient.

A publish/subscribe API may be described as a library that enables anevent publisher, such as publishing device 1022, to publish eventstreams into ESPE 800 or an event subscriber, such as event subscribingdevice A 1024 a, event subscribing device B 1024 b, and eventsubscribing device C 1024 c, to subscribe to event streams from ESPE800. For illustration, one or more publish/subscribe APIs may bedefined. Using the publish/subscribe API, an event publishingapplication may publish event streams into a running event streamprocessor project source window of ESPE 800, and the event subscriptionapplication may subscribe to an event stream processor project sourcewindow of ESPE 800.

The publish/subscribe API provides cross-platform connectivity andendianness compatibility between ESP application and other networkedapplications, such as event publishing applications instantiated atpublishing device 1022, and event subscription applications instantiatedat one or more of event subscribing device A 1024 a, event subscribingdevice B 1024 b, and event subscribing device C 1024 c.

Referring back to FIG. 9, operation 906 initializes thepublish/subscribe capability of ESPE 800. In an operation 908, the oneor more projects 802 are started. The one or more started projects mayrun in the background on an ESP device. In an operation 910, an eventblock object is received from one or more computing device of thepublishing device 1022.

ESP subsystem 800 may include a publishing client 1002, ESPE 800, asubscribing client A 1004, a subscribing client B 1006, and asubscribing client C 1008. Publishing client 1002 may be started by anevent publishing application executing at publishing device 1022 usingthe publish/subscribe API. Subscribing client A 1004 may be started byan event subscription application A, executing at event subscribingdevice A 1024 a using the publish/subscribe API. Subscribing client B1006 may be started by an event subscription application B executing atevent subscribing device B 1024 b using the publish/subscribe API.Subscribing client C 1008 may be started by an event subscriptionapplication C executing at event subscribing device C 1024 c using thepublish/subscribe API.

An event block object containing one or more event objects is injectedinto a source window of the one or more source windows 806 from aninstance of an event publishing application on publishing device 1022.The event block object may generated, for example, by the eventpublishing application and may be received by publishing client 1002. Aunique ID may be maintained as the event block object is passed betweenthe one or more source windows 806 and/or the one or more derivedwindows 808 of ESPE 800, and to subscribing client A 1004, subscribingclient B 806, and subscribing client C 808 and to event subscriptiondevice A 1024 a, event subscription device B 1024 b, and eventsubscription device C 1024 c. Publishing client 1002 may furthergenerate and include a unique embedded transaction ID in the event blockobject as the event block object is processed by a continuous query, aswell as the unique ID that publishing device 1022 assigned to the eventblock object.

In an operation 912, the event block object is processed through the oneor more continuous queries 804. In an operation 914, the processed eventblock object is output to one or more computing devices of the eventsubscribing devices 1024 a-c. For example, subscribing client A 804,subscribing client B 806, and subscribing client C 808 may send thereceived event block object to event subscription device A 1024 a, eventsubscription device B 1024 b, and event subscription device C 1024 c,respectively.

ESPE 800 maintains the event block containership aspect of the receivedevent blocks from when the event block is published into a source windowand works its way through the directed graph defined by the one or morecontinuous queries 804 with the various event translations before beingoutput to subscribers. Subscribers can correlate a group of subscribedevents back to a group of published events by comparing the unique ID ofthe event block object that a publisher, such as publishing device 1022,attached to the event block object with the event block ID received bythe subscriber.

In an operation 916, a determination is made concerning whether or notprocessing is stopped. If processing is not stopped, processingcontinues in operation 910 to continue receiving the one or more eventstreams containing event block objects from the, for example, one ormore network devices. If processing is stopped, processing continues inan operation 918. In operation 918, the started projects are stopped. Inoperation 920, the ESPE is shutdown.

As noted, in some examples, big data is processed for an analyticsproject after the data is received and stored. In other examples,distributed applications process continuously flowing data in real-timefrom distributed sources by applying queries to the data beforedistributing the data to geographically distributed recipients. Asnoted, an event stream processing engine (ESPE) may continuously applythe queries to the data as it is received and determines which entitiesreceive the processed data. This allows for large amounts of data beingreceived and/or collected in a variety of environments to be processedand distributed in real time. For example, as shown with respect to FIG.2, data may be collected from network devices that may include deviceswithin the internet of things, such as devices within a home automationnetwork. However, such data may be collected from a variety of differentresources in a variety of different environments. In any such situation,embodiments of the present technology allow for real-time processing ofsuch data.

Aspects of the present disclosure provide technical solutions totechnical problems, such as computing problems that arise when an ESPdevice fails which results in a complete service interruption andpotentially significant data loss. The data loss can be catastrophicwhen the streamed data is supporting mission critical operations, suchas those in support of an ongoing manufacturing or drilling operation.An example of an ESP system achieves a rapid and seamless failover ofESPE running at the plurality of ESP devices without serviceinterruption or data loss, thus significantly improving the reliabilityof an operational system that relies on the live or real-time processingof the data streams. The event publishing systems, the event subscribingsystems, and each ESPE not executing at a failed ESP device are notaware of or effected by the failed ESP device. The ESP system mayinclude thousands of event publishing systems and event subscribingsystems. The ESP system keeps the failover logic and awareness withinthe boundaries of out-messaging network connector and out-messagingnetwork device.

In one example embodiment, a system is provided to support a failoverwhen event stream processing (ESP) event blocks. The system includes,but is not limited to, an out-messaging network device and a computingdevice. The computing device includes, but is not limited to, aprocessor and a computer-readable medium operably coupled to theprocessor. The processor is configured to execute an ESP engine (ESPE).The computer-readable medium has instructions stored thereon that, whenexecuted by the processor, cause the computing device to support thefailover. An event block object is received from the ESPE that includesa unique identifier. A first status of the computing device as active orstandby is determined. When the first status is active, a second statusof the computing device as newly active or not newly active isdetermined. Newly active is determined when the computing device isswitched from a standby status to an active status. When the secondstatus is newly active, a last published event block object identifierthat uniquely identifies a last published event block object isdetermined. A next event block object is selected from a non-transitorycomputer-readable medium accessible by the computing device. The nextevent block object has an event block object identifier that is greaterthan the determined last published event block object identifier. Theselected next event block object is published to an out-messagingnetwork device. When the second status of the computing device is notnewly active, the received event block object is published to theout-messaging network device. When the first status of the computingdevice is standby, the received event block object is stored in thenon-transitory computer-readable medium.

FIG. 11 is a flow chart of an example of a process for enhancing a powermethod on an electronic device according to some aspects. Some examplescan include more, fewer, or different steps than the steps depicted inFIG. 11. Also, some examples can implement the steps of the process in adifferent order. Some examples can be implemented using any of thesystems and processes described with respect to FIGS. 1-10.

In block 1102, a processor receives an electronic communicationassociated with a job. The processor can receive at least a portion ofthe electronic communication from a local source, such as a user inputdevice (e.g., a keyboard, mouse, touch-screen, etc.); a remote source,such as a remote computing device (e.g., a node, such as a worker nodeor control node discussed with respect to FIG. 4); or both of these.

In some examples, the job can be associated with ranking documents orlinks (e.g., to be output by a search engine), generating recommendedcontent (e.g., songs, images, video content, articles, publications,websites, news stories, etc.) to be provided to a user, or anycombination of these. For example, the processor can form at least aportion of a computing environment for a search engine. The searchengine may receive a query and provide results based on the query. Theresults can include documents, websites, links, or any combination ofthese that are ordered in a particular sequence. In such an example, thejob can include determining the particular sequence in which to orderthe documents, websites, and links.

As another example, the processor can form at least a portion of acomputing environment for a recommendation engine. The recommendationengine may receive information about a user and output recommendedcontent for the user based on the information about the user. Therecommended content can include songs, images, video content, articles,publications, websites, news stories, or any combination of these thatare ordered in a particular sequence. In such an example, the job caninclude determining the particular sequence in which to order the songs,images, video content, articles, publications, websites, news stories,or any combination of these for the recommended content.

In block 1104, the processor determines a best rank-1 approximation of amatrix associated with the job. The matrix can have any number andcombination of columns and rows. In one example, the job can includedetermining a matrix of values associated with search results from asearch engine or recommendations from a recommendation engine. Theprocessor can determine the best rank-1 approximation for the matrix.

The processor can determine the best rank-1 approximation of the matrixusing an enhanced power method (e.g., a modified version of the powermethod). In some examples, the enhanced power method can be implementedaccording to Algorithm 2 defined below:

Input: A, v₀

Output: u_(i), v_(i), λ_(i)

-   -   1: Set i=0    -   2: repeat    -   3: Set i=i+1    -   4: Determine α_(i)    -   5: Set r_(i)=(1−α_(j))v_(i-2)+α_(j)v_(i-1)    -   6:

${{Compute}\mspace{14mu} u_{i}} = \frac{{Ar}_{i}}{{{Ar}_{i}}_{2}}$

-   -   7:

${{Compute}\mspace{14mu} v_{i}} = \frac{A^{T}u_{i}}{{{A^{T}u_{i}}}_{2}}$

-   -   8: Set λ_(i)=u_(i) ^(T)Av_(i)=∥A^(T)u_(i)∥₂    -   9: until a convergence criterion is satisfied        where A is the matrix A; v₀ is an initial, right singular value        that is nonzero; λ_(i) is the largest singular value of the        matrix at interval i; u_(i) is the left singular value at        interval i; v_(i) is the right singular value at interval i;        r_(i) is a point that lies on a line that passes through v_(i-2)        and v_(i-1); and α_(i) is a refinement factor (e.g., discussed        in greater detail below with respect to FIG. 12). By way of        comparison, in Algorithm 2, the value for u_(i) is determined        based on the point r_(i) (which is determined based on the        refinement factor). This is different from Algorithm 1, in which        the value for u_(i) is determined based on v_(i-1).

In some examples, the processor can implement the enhanced power methodby performing one or more of the steps shown in FIG. 12. Turning to FIG.12, in block 1202, the processor determines a refinement factor (α). Forexample, the processor can determine a value for a that maximizes thefollowing univariate function:

$\begin{matrix}{{h(\alpha)} = \frac{{{A\left\lbrack {{\left( {1 - \alpha} \right)v_{i - 2}} + {\alpha\; v_{i - 1}}} \right\rbrack}}_{2}^{2}}{{{{\left( {1 - \alpha} \right)v_{i - 2}} + {\alpha\; v_{i - 1}}}}_{2}^{2}}} & {{Equation}\mspace{14mu} 2}\end{matrix}$

In some examples, Equation 2 can be modified and rewritten such that:

$\alpha = \frac{{- \left( {{a_{1}c_{2}} - {a_{2}c_{1}}} \right)} - \sqrt{\delta}}{{a_{1}b_{2}} - {a_{2}b_{1}}}$

where a₁=∥Av_(i-1)−Av_(i-2)∥₂ ²; a₂=∥v_(i-1)−v_(i-2)∥₂ ²; b₁=∥Av_(i-1)∥₂²−a₁−c₁; b₂=−a₂; c₁=∥Av_(i-2)∥₂ ²; and c₂=1. Because the values forv_(i-1) and v_(i-2) can be known at each iteration, Equations 2 and 3can be solved to determine the refinement factor.

In block 1204, the processor determines a point (r_(i)) on a line thatpasses through two values for a vector from prior iterations of thepower method. The vector can be v and the two values can be v_(i-2) andv_(i-1). For example, as discussed above, r_(i) can equal(1−α_(i))v_(i-2)+α_(i)v_(i-1). The processor can determine r_(i) bycalculating (1−α_(i))v_(i-2)+α_(i)v_(i-1).

In block 1206, the processor performs a power method using the point.For example, the processor can implement the enhanced power methoddefined by Algorithm 2 using the point. The results from Algorithm 2 canbe values for u_(i), v_(i), and λ_(i) that satisfy (e.g., optimize)Equation 1 for determining the best rank-1 approximation of the matrix.

As a particular example, the matrix (A) that is associated with the jobcan have the following values:

$A = \begin{bmatrix}1 & 2 & 0 & 2 \\2 & {- 3} & {- 2} & 3 \\3 & {- 1} & 1 & 1\end{bmatrix}$

In some examples, a traditional power method defined by Algorithm 1 canbe applied to matrix A (with v₀ set to be the first row of matrix A).The results for the first 12 iterations of the traditional power methodare shown in table 1300 of FIG. 13. In table 1300, column 1302 includesthe values for u_(i), column 1304 includes the values for v_(i), andcolumn 1306 includes the values for λ_(i). There can be three values incolumn 1302 because there are three rows in matrix A. There can be fourvalues in column 1304 because there are four columns in matrix A. Thevalues shown in the 12^(th) row of columns 1302, 1304, and 1306 foru_(i), v_(i), and λ_(i), respectively, can be input into Equation 1 todetermine the best rank-1 approximation for matrix A.

In other examples, the enhanced power method defined by Algorithm 2 canbe applied to matrix A. The results of the first 8 iterations of theenhanced power method are shown in table 1400 of FIG. 14. In table 1400,column 1402 includes the values for u_(i), column 1404 includes thevalues for v_(i), and column 1406 includes the values for λ_(i). Lookingat FIGS. 13-14 together, it can be seen that the enhanced power methodcan require fewer iterations than the traditional power method.Specifically, the traditional power method takes 11 iterations toachieve a λ value of 5.62580065, whereas the enhanced power method takes6 iterations to achieve the same λ value. In FIGS. 13-14, the rowscorresponding to i=1 are identical because α₁=1 in the enhanced powermethod, and both power methods started with the same initializationpoint.

In some examples, the enhanced power method can be more effective whenthe value for α_(i) is significantly greater than 1. For example, if avalue of α₂=3.62700438 is plugged in to Algorithm 2, λ₂ can equal5.59802814, which is considerably greater than the corresponding valuefor λ₂ (e.g., 5.11330892) in the traditional power method. This may bebecause, when the value of α_(i) is greater than 1, the point (r_(i))can be extrapolated beyond v_(i-1) along the direction ofv_(i-1)−v_(i-2). When α_(i) is less than 1, the point (r_(i)) can beinterpolated between v_(i-2) and v_(i-1), taking a more cautious step.The extrapolation can reduce the number of iterations performed by theenhanced power method. This is because the enhanced power method takesadvantage of a continuation property (e.g., that the values of u_(i) andv_(i) continue to increase, or continue to decrease,iteration-after-iteration) in the values for u_(i) and v_(i) obtainedusing the traditional power method. This continuation property isobservable in the values for u_(i) and v_(i) in FIG. 13.

Although an iteration of the enhanced power method can have a highercomputational cost than an iteration of the traditional power method,the additional computational cost can be almost negligible. For example,a matrix A can have m rows and n columns. A comparison of thecomputational costs for performing the traditional power method and theenhanced power method on dense and sparse versions of the matrix A areshown in the table 1500 of FIG. 15. The computational cost forperforming the traditional power method on matrix A is shown in column1502. The computational cost for performing the enhanced power method onmatrix A is shown in column 1504. The difference between the two can be3m+2n computations, as shown in column 1506. This difference is verysmall and almost negligible. For example, in the dense version of matrixA, the factor of 2mn has the greatest impact on the computational costfor both the traditional power method and the enhanced power method. Andthe additional computational cost of 3m+2n to perform the enhanced powermethod is almost negligible.

Further, the additional computational cost for each iteration of theenhanced power method can be offset by the significant reduction in thetotal number of iterations performed using the enhanced power method. Asa particular example, FIG. 16 shows data sets used to compare thetraditional power method against the enhanced power method. Column 1602indicates whether a matrix of the data set is sparse or dense. Column1604 indicates a number of rows in the matrix. Column 1606 indicates anumber of columns in the matrix. Column 1608 indicates a number ofnonzero entries in the matrix. FIG. 17 shows a table 1700 of an exampleof results from analyzing the data sets in FIG. 16 using the traditionalpower method and the enhanced power method. Column 1702 represents aniteration number. Columns 1704-1710 show the results for each respectivedata set. Within each of the columns 1704-1710 (e.g., within column1704), the left-most column indicates the number of iterations used bythe traditional power method, the middle column indicates the number ofiterations used by the enhanced power method, and the right columnindicates a ratio of the leading two eigenvalues associated with thematrix. It can be seen that when the ratio of the eigenvalues is a lowernumber (e.g., farther from one), the traditional power method and theenhanced power method converge in fewer iterations. When the ratio ofthe eigenvalues is a higher number, the traditional power method and theenhanced power method converge after a higher number of iterations.

The last row of table 1700 shows the total number of iterations usingthe traditional power method and the enhanced power method. The enhancedpower method only takes 23% of the iterations performed by thetraditional power method for the Webspam data set. The enhanced powermethod only takes 31% of the iterations performed by the traditionalpower method for the Real-sim data set. The enhanced power method onlytakes 36% of the iterations performed by the traditional power methodfor the Url data set. And the enhanced power method only takes 28% ofthe iterations performed by the traditional power method for the KDD2010data set. Thus, the amount of processing power and the number of memoryaccesses required for performing the enhanced power method can besignificantly less than are required for the traditional power method.

In some examples, the fewer iterations performed using the enhancedpower method can result in a reduced amount of latency in a system. Forexample, a system may include multiple nodes (e.g., the worker nodes andcontrol nodes discussed with respect to FIG. 4). The nodes can worktogether to perform a power method for determining a best rank-1approximation of a matrix. For example, some or all of the nodes cantransmit and receive information associated with the power method or thebest rank-1 approximation of the matrix. Examples of the information caninclude the best rank-1 approximation of the matrix, a current value forthe left singular value (u) in a current iteration, a current value forthe right singular value (v_(i)) in the current iteration, a currentvalue for λ in the current iteration, a current value for a refinementfactor (α) in the current iteration, a value (e.g., v_(i-1)) for theright singular vector from an immediately prior iteration of the powermethod, a value (e.g., v_(i-2)) for the right singular vector fromanother prior iteration of the power method, or any combination ofthese. Each communication can take a period of time to complete. Becausethere may be more iterations required for the traditional power method,there may be more communications and more resulting latency in thesystem if the nodes perform the traditional power method. Conversely,because there may be fewer iterations required for the enhanced powermethod, there can be fewer communications and less resulting latency inthe system if the nodes perform the enhanced power method.

Returning now to FIG. 11, in block 1106, the processor performs the jobbased on the best rank-1 approximation of the matrix. For example, thejob can be associated with generating a model. The model can represent arelationship between data included in the electronic communication andmultiple independent variables that influence the data. The processorcan generate the model using the best rank-1 approximation of thematrix. For example, the processor can provide the best rank-1approximation of the matrix as input to a modeling program or apply thebest rank-1 approximation of the matrix to an algorithm to generate themodel.

In block 1108, the processor transmits another electronic communicationassociated with the job. In some examples, the other electroniccommunication can include a result of the job. For example, theprocessor can transmit a display signal, which can be the otherelectronic communication, to a display device (e.g., a computer monitor)to cause the display device to output a graphical representation of theresult of the job.

In some examples, the processor can transmit the other electroniccommunication to a worker node or a control node (e.g., as discussedwith respect to FIG. 4). The electronic communication can includeinformation associated with the power method or the best rank-1approximation of the matrix. For example, the information can includethe best rank-1 approximation of a matrix, a current value for the leftsingular value (u) in a current iteration of the power method, a currentvalue for the right singular value (v_(i)) in the current iteration, acurrent value for λ in the current iteration, a current value for arefinement factor (α) in the current iteration, or any combination ofthese.

The foregoing description of certain examples, including illustratedexamples, has been presented only for the purpose of illustration anddescription and is not intended to be exhaustive or to limit thedisclosure to the precise forms disclosed. Numerous modifications,adaptations, and uses thereof will be apparent to those skilled in theart without departing from the scope of the disclosure.

The invention claimed is:
 1. A non-transitory computer readable mediumcomprising: program code executable by a processor for causing theprocessor to receive an electronic communication indicating a job to beperformed; program code executable by the processor for causing theprocessor to determine a best rank-1 approximation of a matrixassociated with the job using a power method, wherein each iteration ofthe power method comprises: determining a point that lies on a linepassing through (i) a first value for a first singular vector from animmediately prior iteration of the power method; and (ii) a second valuefor the first singular vector from another prior iteration of the powermethod; and determining, by performing the power method using the point,a current value for the first singular vector and a current value for asecond singular vector for a current iteration of the power method;program code executable by the processor for causing the processor toperform the job at least in part using the best rank-1 approximation ofthe matrix; and program code executable by the processor for causing theprocessor to transmit another electronic communication associated with aresult of the job.
 2. The non-transitory computer readable medium ofclaim 1, further comprising program code executable by the processor forcausing the processor to determine the point based on a refinementfactor, the refinement factor being a value that maximizes a functionthat includes a predetermined relationship between (i) the matrix; (ii)the first value for the first singular vector from the immediately prioriteration of the power method, and (iii) the second value for the firstsingular vector from the other prior iteration of the power method. 3.The non-transitory computer readable medium of claim 2, wherein thefirst singular vector is a left singular vector for the matrix and thesecond singular vector is a right singular vector for the matrix.
 4. Thenon-transitory computer readable medium of claim 3, wherein the job isassociated with ranking documents or links in a search engine orgenerating recommended content to be provided to a user.
 5. Thenon-transitory computer readable medium of claim 1, wherein the job isassociated with generating a model that represents a relationshipbetween data included in the electronic communication and a plurality ofindependent variables that influence the data.
 6. The non-transitorycomputer readable medium of claim 1, wherein the power method isconfigured to use a lower number of computational iterations fordetermining the best rank-1 approximation of the matrix than anotherpower method in which the current value for the first singular vectorand the current value for the second singular vector are determinedexclusive of the second value for the first singular vector from theother prior iteration of the power method.
 7. The non-transitorycomputer readable medium of claim 1, wherein the power method isconfigured to use less memory for storing data associated withperforming the power method than another power method in which thecurrent value for the first singular vector and the current value forthe second singular vector are determined exclusive of the second valuefor the first singular vector from the other prior iteration of thepower method.
 8. The non-transitory computer readable medium of claim 1,further comprising program code executable by the processor for causingthe processor to communicate at least one of the best rank-1approximation of the matrix, the current value for the first singularvector, or the current value for the second singular vector to a workernode in a communications grid computing system for performing the job.9. The non-transitory computer readable medium of claim 8, furthercomprising program code executable by the processor for causing theprocessor to receive the electronic communication from the worker nodein the communications grid computing system, the electroniccommunication comprising at least one of the first value for the firstsingular vector from the immediately prior iteration of the powermethod, or the second value for the first singular vector from the otherprior iteration of the power method.
 10. The non-transitory computerreadable medium of claim 1, further comprising program code executableby the processor for causing the processor to transmit the otherelectronic communication associated with the result of the job bytransmitting a display signal configured to cause a display device tooutput a graphical representation of the result of the job.
 11. Acomputer-implemented method executed by a processing device coupled to amemory device, the computer-implemented method comprising: receiving, bythe processing device, an electronic communication indicating a job tobe performed; determining, by the processing device, a best rank-1approximation of a matrix associated with the job using a power method,wherein each iteration of the power method comprises: determining apoint that lies on a line passing through (i) a first value for a firstsingular vector from an immediately prior iteration of the power method;and (ii) a second value for the first singular vector from another prioriteration of the power method; and determining, by performing the powermethod using the point, a current value for the first singular vectorand a current value for a second singular vector for a current iterationof the power method; performing, by the processing device, the job atleast in part using the best rank-1 approximation of the matrix; andtransmitting, by the processing device, another electronic communicationassociated with a result of the job.
 12. The computer-implemented methodof claim 11, further comprising determining the point based on arefinement factor, the refinement factor being a value that maximizes afunction that includes a predetermined relationship between (i) thematrix; (ii) the first value for the first singular vector from theimmediately prior iteration of the power method, and (iii) the secondvalue for the first singular vector from the other prior iteration ofthe power method.
 13. The computer-implemented method of claim 12,wherein the first singular vector is a left singular vector for thematrix and the second singular vector is a right singular vector for thematrix.
 14. The computer-implemented method of claim 11, wherein the jobis associated with ranking documents or links in a search engine orgenerating recommended content to be provided to a user.
 15. Thecomputer-implemented method of claim 11, wherein the job is associatedwith generating a model that represents a relationship between dataincluded in the electronic communication and a plurality of independentvariables that influence the data.
 16. The computer-implemented methodof claim 11, wherein the power method is configured to use a lowernumber of computational iterations for determining the best rank-1approximation of the matrix than another power method in which thecurrent value for the first singular vector and the current value forthe second singular vector are determined exclusive of the second valuefor the first singular vector from the other prior iteration of thepower method.
 17. The computer-implemented method of claim 11, whereinthe power method is configured to use less memory for storing dataassociated with performing the power method than another power method inwhich the current value for the first singular vector and the currentvalue for the second singular vector are determined exclusive of thesecond value for the first singular vector from the other prioriteration of the power method.
 18. The computer-implemented method ofclaim 11, wherein further comprising communicating at least one of thebest rank-1 approximation of the matrix, the current value for the firstsingular vector, or the current value for the second singular vector toa worker node in a communications grid computing system for performingthe job.
 19. The computer-implemented method of claim 18, furthercomprising receiving the electronic communication from the worker nodein the communications grid computing system, the electroniccommunication comprising at least one of the first value for the firstsingular vector from the immediately prior iteration of the powermethod, or the second value for the first singular vector from the otherprior iteration of the power method.
 20. The computer-implemented methodof claim 18, further comprising transmitting the other electroniccommunication associated with the result of the job by transmitting adisplay signal configured to cause a display device to output agraphical representation of the result of the job.
 21. A systemcomprising: a processing device; and a memory device in whichinstructions executable by the processing device are stored for causingthe processing device to: receive an electronic communication indicatinga job to be performed; determine a best rank-1 approximation of a matrixassociated with the job using a power method, wherein each iteration ofthe power method comprises: determining a point that lies on a linepassing through (i) a first value for a first singular vector from animmediately prior iteration of the power method; and (ii) a second valuefor the first singular vector from another prior iteration of the powermethod; and determining, by performing the power method using the point,a current value for the first singular vector and a current value for asecond singular vector for a current iteration of the power method;perform the job at least in part using the best rank-1 approximation ofthe matrix; and transmit another electronic communication associatedwith a result of the job.
 22. The system of claim 21, wherein the memorydevice further comprises instructions executable by the processingdevice for causing the processing device to determine the point based ona refinement factor, the refinement factor being a value that maximizesa function that includes a predetermined relationship between (i) thematrix; (ii) the first value for the first singular vector from theimmediately prior iteration of the power method, and (iii) the secondvalue for the first singular vector from the other prior iteration ofthe power method.
 23. The system of claim 22, wherein the first singularvector is a left singular vector for the matrix and the second singularvector is a right singular vector for the matrix.
 24. The system ofclaim 23, wherein the job is associated with ranking documents or linksin a search engine or generating recommended content to be provided to auser.
 25. The system of claim 21, wherein the job is associated withgenerating a model that represents a relationship between data includedin the electronic communication and a plurality of independent variablesthat influence the data.
 26. The system of claim 21, wherein the powermethod is configured to use a lower number of computational iterationsfor determining the best rank-1 approximation of the matrix than anotherpower method in which the current value for the first singular vectorand the current value for the second singular vector are determinedexclusive of the second value for the first singular vector from theother prior iteration of the power method.
 27. The system of claim 21,wherein the power method is configured to use less memory for storingdata associated with performing the power method than another powermethod in which the current value for the first singular vector and thecurrent value for the second singular vector are determined exclusive ofthe second value for the first singular vector from the other prioriteration of the power method.
 28. The system of claim 21, wherein thememory device further comprises instructions executable by theprocessing device for causing the processing device to communicate atleast one of the best rank-1 approximation of the matrix, the currentvalue for the first singular vector, or the current value for the secondsingular vector to a computing device for performing the job.
 29. Thesystem of claim 28, wherein the memory device further comprisesinstructions executable by the processing device for causing theprocessing device to receive the electronic communication from theworker node in the communications grid computing system, the electroniccommunication comprising at least one of the first value for the firstsingular vector from the immediately prior iteration of the powermethod, or the second value for the first singular vector from the otherprior iteration of the power method.
 30. The system of claim 21, whereinthe memory device further comprises instructions executable by theprocessing device for causing the processing device to transmit theother electronic communication associated with the result of the job bytransmitting a display signal configured to cause a display device tooutput a graphical representation of the result of the job.